FIG. 1 shows the typical inverter configuration and current commutation sequence for a brushless sensorless DC (BLDC) motor. Generally, a brushless DC motor is driven by three phase inverter (motor drive circuit) by applying three voltage profiles on the three phase that will result in each phase current profile being three sine wave each 120° electrical angle phase apart from each other. In an ideal motor, the Bemf in each phase will track the phase of its current. The zero crossing of this Bemf signal can be measured by first anticipating when the zero crossing is about to occur, and then opening a “window” by floating the motor phase corresponding to the zero cross to make a back EMF detection measurement in the floating winding.
FIG. 2 illustrates a conventional back EMF detection circuit 10 for a floating winding measurement. The circuit 10 includes a differential amplifier 12 having a first (negative) input terminal coupled to the center tap CT of the motor 14. The differential amplifier 12 further includes a second (positive) input terminal coupled to the coil tap of motor phase C. The assumption here is that the measurement is made with respect to motor phase C presenting the floating third phase. The following equation applies:Vc−Vct=BemfC+(Rm×Ic)+(L×dIc/dt)
If motor phase C is the floating third phase (i.e., the commutation phase sequence is at AB), and if the differential amplifier 12 has a high input impedance, the current flowing through motor phase C is Ic=0. The foregoing equation thus simplifies to:BemfC=Vc−Vct 
As is known to those skilled in the art, a BLDC motor in many instances does not include an externally accessible center tap CT connection. The implementation of FIG. 2 therefore cannot be used for measuring back EMF.
FIG. 3 illustrates a conventional back EMF detection circuit 20 using a three phase virtual center tap measurement configuration. Again, the floating third phase opens a window to make a back EMF detection measurement in the floating winding. The circuit 20 includes a differential amplifier 22 having a first (negative) input terminal coupled to a three phase virtual center tap VCT of the motor 24. A first sense resistor Rs is coupled between the coil tap of motor phase C and the three phase virtual center tap VCT. A second sense resistor Rs is coupled between the coil tap of motor phase B and the three phase virtual center tap VCT. A third sense resistor Rs is coupled between the coil tap of motor phase A and the three phase virtual center tap VCT. It will accordingly be understood that the phrase “three phase virtual center tap” refers to and means a virtual center tap circuit coupled to three motor phases. The differential amplifier 12 further includes a second (positive) input terminal coupled to the coil tap of motor phase C (the floating phase). The assumption here is that the measurement is made with respect to motor phase C presenting the floating third phase. The following equations apply:Vvct=(Va+Vb+Vc)/3Vvct=(BemfA+BemfB+BemfC+Rm(Ia+Ib+Ic))/3+Vct Vc−Vvct=⅔(BemfC+Rm×Ic)−⅓(BemfA+BemfB+Rm(Ia+Ib))Vc−Vvct=BemfC+Rm/3(2Ic−Ia−Ib)Vc−Vvct=BemfC+Rm/3(3Ic)Vc−Vvct=BemfC+Rm×Ic 
Because the comparator is usually designed with high input impedance, the current Ic in the floating phase can theoretically be ignored and the foregoing equations simplify to:BemfC=Vc−Vvct 
More generally, let Iext be the current sourced from Vc from external devices (e.g., the comparator input or spindle driver leakage, etc.). Applying Kirchhoff's current law on the node for the coil tap of motor phase C, the following equations apply:Ic=(Vb+Va−2Vvct)/(2Rs)−Iext Ic=(Vb+Va−⅔(Va+Vb+Vc))/Rs−Iext Ic=−BemfC/(Rs+Rm)−Rs/(Rs+Rm)Iext Vc−Vvct=Rs/(Rs+Rm)BemfC−RmRs/(Rs+Rm)Iext 
The resistance Rs is generally chosen such that Rs>>Rm and Iext is approximately zero. The foregoing thus reduces to:BemfC=Vc−Vvct 